By Panos Macheras, Athanassios Iliadis
The cutting-edge in Biopharmaceutics, Pharmacokinetics, and Pharmacodynamics Modeling is gifted during this ebook. It indicates how complex actual and mathematical tools can extend classical versions on the way to hide heterogeneous drug-biological procedures and healing results within the physique. The booklet is split into 4 elements; the 1st offers with the basic rules of fractals, diffusion and nonlinear dynamics; the second one with drug dissolution, unencumber, and absorption; the 3rd with empirical, compartmental, and stochastic pharmacokinetic types, and the fourth normally with nonclassical features of pharmacodynamics. The classical types that experience relevance and alertness to those sciences also are thought of all through. Many examples are used to demonstrate the intrinsic complexity of drug management similar phenomena within the human, justifying using complex modeling equipment.
This well timed and important e-book will attract graduate scholars and researchers in pharmacology, pharmaceutical sciences, bioengineering, and physiology.
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Additional info for Modeling in Biopharmaceutics, Pharmacokinetics, and Pharmacodynamics: Homogeneous and Heterogeneous Approaches
5. FRACTAL-LIKE KINETICS down, since as reactants get further apart, they must travel longer distances to find another reactant to react with (cf. 9). A curious effect now is that the rate constant k of the reaction is no longer “constant”, but depends on the growth of this depletion zone and consequently is time-dependent: k (t) = k◦ t−λ (t > t◦ ), where k (t) is the instantaneous rate coefficient since it depends on time t, and λ is the fractal kinetics exponent with 0 ≤ λ < 1. In fact, k (t) crosses over from a constant regime at short times, t < t◦ , to a power-law decrease at longer times, t > t◦ .
This happens when c is a linear function of z (∂c/∂z is constant). Under these conditions, as many drug molecules diffuse in from the side of higher concentration as diffuse out from the side of lower concentration. , cl and cr are kept fixed. 4 A. 4 B). In reality, plot A is the asymptotic behavior of the general case B as t goes to infinity. 17) δ cr (t) cos iπ − cl (t) z D exp − 2 i2 π 2 t . 17). If we postulate that molecules move independently, the concentration c (z, t) at some point z is proportional to the probability density p (z, t) of finding a molecule there.
593 for the 2-dimensional site model. Also, the percolation thresholds vary according to the type of model (site or bond) as well as with the dimensionality of the lattice (2 or 3). 7. 6. Only the occupied sites that belong to the percolating cluster are shown. The most remarkable properties of percolation clusters arise from their sudden inception when the bond concentration (probability) reaches the critical threshold value p = pc . At this specific value the emerged cluster spans two opposite sides of the lattice and if one conceives of the bonds as channels, the cluster allows a fluid to flow through the medium from edge to edge.